Subspace clustering guided convex nonnegative matrix factorization

As one of the most important information of the data, the geometry structure information is usually modeled by a similarity graph to enforce the effectiveness of nonnegative matrix factorization (NMF). However, pairwise distance based graph is sensitive to noise and can not capture the subspace structure of the data. Reconstruction coefficients based graph can capture the subspace structure of the data, but the procedure of building the representation based graph is usually independent to the framework of NMF. To address this issue, a novel subspace clustering guided convex nonnegative matrix factorization (SC-CNMF) is proposed. In this NMF framework, the nonnegative subspace clustering is incorporated to learning the representation based graph, and meanwhile, a convex nonnegative matrix factorization is also updated simultaneously. To tackle the noise influence of the dataset, only k largest entries of each representation are kept in the subspace clustering. To capture the complicated geometry structure of the data, multiple centroids are also introduced to describe each cluster. Additionally, a row constraint is used to remove the relevance among the rows of the encoding matrix, which can help to improve the clustering performance of the proposed model. For the proposed NMF framework, two different objective functions with different optimizing schemes are designed. Image clustering experiments are conducted to demonstrate the effectiveness of the proposed methods on several datasets and compared with some related works based on NMF together with k-means clustering method and PCA as baseline.